Minimum density of triangulated packing’s three different size circles

Abstract

The results of a study to determine the minimum and maximum packing density of disks are presented. The minimum and maximum packing densities of disks of three different sizes on a torus are determined. The minimum density is obtained from the ratio of the sectors of the circle to all parts of the triangle on the torus. Heron’s formula is used to find the minimum and maximum density of triangular packing. A diagram of a triangle formed by combining the centers of three circles of three mutually tangent circles and the minimum triangular packing density is given.